Find the smallest no by which 15250 should be divided to make a perfect cube
Answers
Ncert solutions
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Mathematics
Science
Chapters in NCERT Solutions - Mathematics , Class 8
Exercises in Cubes and Cube Roots
Question 6
Q3) Find the smallest number by which each of the following numbers must be divided to obtain a perfect cube:
(i)81
(ii)128
(iii)135
(iv)192
(v)704
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Solution:
(i)81
Prime factors of 81 = 3\times3\times3\times33×3×3×3
Here one factor 3 is not grouped in triplets.
Therefore 81 must be divided by 3 to make it a perfect cube.
(ii) 128
Prime factors of 128 = 2\times2\times2\times2\times2\times22×2×2×2×2×2
Here one factor 2 does not appear in a 3’s group.
Therefore, 128 must be divided by 2 to make it a perfect cube.
(iii) 135
Prime factors of 135 = 3\times3\times3\times53×3×3×5
Here one factor 5 does not appear in a triplet.
Therefore, 135 must be divided by 5 to make it a perfect cube.
(iv) 192
Prime factors of 192 = 2\times2\times2\times2\times2\times32×2×2×2×2×3
Here one factor 3 does not appear in a triplet.
Therefore, 192 must be divided by 3 to make it a perfect cube.
Answer:
122
Step-by-step explanation:
15250 = 2*5*5*5*61
So we have to divide by = 2*61
= 122
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